While chaos's answerchaos's answer is good to be used in interactive shells, this one can be used as a POSIX script, for example if you need to do this periodically and/or do it on another computers.
#!/bin/sh
i=0
while test "$((i+=1))" -lt 366 ; do
    for j in 00 06 12 18 ; do
        file="GLDAS_NOAH025SUBP_3H.A2003$(printf '%03d' "$i").${j}00.001.2015210044609.pss.grb"
        test -e "$file" || echo "$file"
    done
done
(seq or brace expansion aren't specified by POSIX.)